Interactions of like-charged rods at low temperatures: analytical theory vs. simulations

Ion-mediated interactions between like-charged polyelectrolytes with bending flexibility

Ion-mediated interactions between polyelectrolytes (PEs) are crucial to the properties of flexible biopolymers such as nucleic acids and proteins but the effect of PE flexibility on such interactions has not been explicitly addressed until now. In this work, the potentials of mean force (PMFs) between like-charged PEs with different bending flexibility have been investigated by Monte Carlo simulations and a cylindrical confinement around each PE was involved to model two PEs in an array. We found that in the absence of trivalent salt, the PMFs between like-charged PEs in an array are apparently repulsive while the bending flexibility can visibly decrease the repulsive PMFs. With the addition of high trivalent salt, the PMFs become significantly attractive whereas the attractive PMFs can be apparently weakened by the bending flexibility. Our analyses reveal that the effect of bending flexibility is attributed to the increased PE conformational space, which allows the PEs to fluctuate away to decrease the monovalent ion-mediated repulsion or to weaken the trivalent ion-mediated attraction through disrupting trivalent ion-bridging configuration. Additionally, our further calculations show that the effect of bending flexibility on the ion-mediated interactions is less apparent for PEs without cylindrical confinement.

Multivalent counterions induced attraction between DNA polyelectrolytes

In this paper we study the electrostatic attraction between two parallel rodlike DNA polyelectrolytes induced by neutralizing multivalent counterions at the zero temperature limit. The counterions crystallize on the charged surfaces of DNA so that we can handle the system by using the Wigner crystal lattice model. We derived the 3D ground state configuration of counterions with minimized energy by use of the gradient descent method, and calculated the interaction between two DNA cylinders with divalent or trivalent counterions when they approach. The results show that the complex ground state configuration of counterions plays a key role in determining the caused attraction. The counterions form three-dimensional Wigner crystals on each cylinder at large separation. When the cylinders are brought together, some counterion lines will move towards the inner region and lead to strong attraction. The calculated interaction from our model is in good agreement with the simulation result, however, the single particle approximation considerably overestimates the attraction.

Counterions in the ground state partially condense in the intervening region of two approaching DNA cylinders and result in attraction.

Charged nanorods at heterogeneously charged surfaces

We study the spatial and orientational distribution of charged nanorods (rodlike counterions) as well as the effective interaction mediated by them between two plane-parallel surfaces that carry fixed (quenched) heterogeneous charge distributions. The nanorods are assumed to have an internal charge distribution, specified by a multivalent monopolar moment and a finite quadrupolar moment, and the quenched surface charge is assumed to be randomly distributed with equal mean and variance on the two surfaces. While equally charged surfaces are known to repel within the traditional mean-field theories, the presence of multivalent counterions has been shown to cause attractive interactions between uniformly charged surfaces due to the prevalence of strong electrostatic couplings that grow rapidly with the counterion valency. We show that the combined effects due to electrostatic correlations (caused by the coupling between the mean surface field and the multivalent, monopolar, charge valency of counterions) as well as the disorder-induced interactions (caused by the coupling between the surface disorder field and the quadrupolar moment of counterions) lead to much stronger attractive interactions between two randomly charged surfaces. The interaction profile turns out to be a nonmonotonic function of the intersurface separation, displaying an attractive minimum at relatively small separations, where the ensuing attraction can exceed the maximum strong-coupling attraction (produced by multivalent monopolar counterions between uniformly charged surfaces) by more than an order of magnitude.

Role of geometrical shape in like-charge attraction of DNA

While the phenomenon of like-charge attraction of DNA is clearly observed experimentally and in simulations, mean-field theories fail to predict it. Kornyshev et al. argued that like-charge attraction is due to DNA's helical geometry and hydration forces. Strong-coupling (SC) theory shows that attraction of like-charged rods is possible through ion correlations alone at large coupling parameters, usually by multivalent counterions. However for SC theory to be applicable, counterion-counterion correlations perpendicular to the DNA strands need to be sufficiently small, which is not a priori the case for DNA even with trivalent counterions. We study a system containing infinitely long DNA strands and trivalent counterions by computer simulations employing varying degrees of coarse-graining. Our results show that there is always attraction between the strands, but its magnitude is indeed highly dependent on the specific shape of the strand. While discreteness of the charge distribution has little influence on the attractive forces, the role of the helical charge distribution is considerable: charged rods maintain a finite distance in equilibrium, while helices collapse to close contact with a phase shift of π, in full agreement with SC predictions. The SC limit is applicable because counterions strongly bind to the charged sites of the helices, so that helix-counterion interactions dominate over counterion-counterion interactions. Thus DNA's helical geometry is not crucial for like-charge DNA attraction, but strongly enhances it, and electrostatic interactions in the strong-coupling limit are sufficient to explain this attraction.

Density functional analysis of like-charged attraction between two similarly charged cylinder polyelectrolytes

A systematic theoretical investigation is performed for electrostatic potential of mean force (EPMF) between two similarly charged rods (modeling DNA) immersed in a primitive model electrolyte solution. Two scientific anomalies are disclosed: (i) although a like-charge attraction (LCA) generally becomes stronger with bulk electrolyte concentration, the opposite effect unexpectedly occurs if the two rod surfaces involved are sufficiently charged and (2) contrary to what is often asserted, that the presence of multivalent counterion is necessary to induce the LCA, it is found that the univalent counterion induces the LCA solely only if bulk electrolyte concentration rises sufficiently and the rod surface charge quantities are high. On the basis of the system energetics calculated first by a classical density functional theory in three-dimensional space, a hydrogen-bonding style mechanism is advanced to reveal the origin of the LCA, and by appealing to fairly common-sense concepts such as bond energy, bond length, number of hydrogen bonds formed, and counterion single-layer saturation adsorption capacity, the present mechanism successfully explains the scientific anomalies and effects of counterion and co-ion diameters in eliciting the LCA first investigated in this work. To add weight to the hydrogen-bonding style mechanism, a theoretical investigation is further performed regarding the effects of the rod surface charge density, co-ion valence, relative permittivity of the medium, temperature, nonelectrostatic interion interactions, and rod diameter in modifying the EPMF, and several novel phenomena are first confirmed, which is self-consistently explained by the present hydrogen-bonding style mechanism.

Macroion solutions in the cell model studied by field theory and Monte Carlo simulations

Aqueous solutions of charged spherical macroions with variable dielectric permittivity and their associated counterions are examined within the cell model using a field theory and Monte Carlo simulations. The field theory is based on separation of fields into short- and long-wavelength terms, which are subjected to different statistical-mechanical treatments. The simulations were performed by using a new, accurate, and fast algorithm for numerical evaluation of the electrostatic polarization interaction. The field theory provides counterion distributions outside a macroion in good agreement with the simulation results over the full range from weak to strong electrostatic coupling. A low-dielectric macroion leads to a displacement of the counterions away from the macroion.